COSMOLOGY

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cosmology cosmology cosmology gravity gravity big bang big bang

TOPICS

GRAVITY BASICS

PROVING BIG BANG THEORY

COSMIC BACKGROUND RADIATION

REDSHIFT

FINAL COMMENT

SOME INTERESTING FACTS

EQUATIONS

BIBLIOGRAPHY

GRAVITY BASICS

Using observation, people starting developing physics without even using any mathematics to predict the outcome.
Physics may have started from the simple lever for mechanical advantage (the longer the lever, the less work)
or from the flight of a spear (greater the angle leadying up to 45°). One of the simplest machines invented is
the incline plane. Using an incline plane, effort of moving a heavy object upwards was lighter work, if the
distance was increased. The example of this can be produced using a ramp. Without a ramp, moving a 50kg barrel
to a height of 1 metre will need an effort of 50kg upwrads. Using a ramp gives the following outcomes:
Example 1 - 2 metre long Ramp to a height of 1 metre.
The 50kg barrel will have to travel (rolled) 2 metres.
The effort required will be 50% of the object (only 25kg), although the taken will be longer.
"picture"
GIVEN #2: Distance rolled = 3 feet to a height of 1 foot.
EFFORT = 20 pounds or 1/3 of 60.
GIVEN #3: Distance rolled = 4 feet to a height of 1 foot.
EFFORT = 15 pounds or 1/4 of 60.
GALILEO GALILEE (1564-1642)
The founder of modern scientist through experiment.

Galileo supposedly dropped two different size weights, one twice the weight of the other, from the Leaning Tower of Pisa. It was thought, at the time, that the weight which was twice the weight of the other would fall twice as fast.

Galileo was to correct the philosophical errors of Aristotle which had been around for twenty centuries. Galileo was the first to test many laws through experiment.

Galileo refused to attend the lectures of Copernicus when they visited Florence, but later was greatly disappointed, when conversing with someone who had now adopted the teachings and he saw the overwhelming evidence which supported the lectures.

Galileo found out Jansen, a Dutchman, had contrived an instrument which brought objects closer when looking through it. With his own knowledge of optics, he was able to make his own and immediately realised the high value of such an instrument within astronomy.

On the 8th of January 1610 Galileo first turned his telescope to look at Jupiter and over the next four nights, one being cloudy, he realised the four stars next to Jupiter where not fixed, but moons encaptured in Jupiter's gravity.

SIR ISAAC NEWTON (1642-1727)
English mathematician. One of the greatest scientists of all time.

Isaac Newton had three main discoveries. He showed that white light is made up from a mixture of colours; he discovered the law of gravitation and the laws of motion that now bear his name; and he also invented calculus the mathematical tool for studying motion. He made all these discoveries before he was 24 years old.

Some other information about what Newton achieved:

- Newton's law of gravitation was the fourth link in a chain of great discoveries in astronomy.

- Newton was the first person to weigh the Sun. He did this mathematically using his law of gravitation.

- Newton found the mathematical strength of the pull of the Sun on the planets.

- Newton invented the reflecting telescope using a curved mirror instead of a lens.

- The discovery of the rocket meant the 300 year old laws discovered by Newton could be used to send man to the Moon.

- Newton, and German philosopher Leibnitz, invented an efficient method of averaging falling objects. It shows that the speed of a falling body is 32 times the number of seconds it has fallen. The branch of mathematics that uses the method of Newton and Leinitz is call differential calculus. Calculus was needed to figure out how fast the Sputnik satellite was travelling around the Earth since its speed was changing all the time.

When Newton brought out his book the Principia Mathematica in 1687, he showed how a long range force called gravity kept the Earth and planets in orbit around the Sun. As stated previously, the greater the mass of an object, the greater the force pulling them together. This can be noted in today's technology of finding planets outside of our own Solar System by measuring the wobble of a distant star. The tell-tale wobble is caused by an object pulling on the star's mass as it orbits. The object is presumably a planet. See Newton's Law of Gravity Acceleration equation.

Gravity g can be stated as a force as follows:

g approx. equal to 9.8Nkg near the Earth's surface.
That is 1kg of mass experiences a force of 9.8N. Hence the following equation.

gravity = force/mass or force = mass x gravity

See Force of Gravity on Earth* equation.

Newton likened the effect of gravity to a lamp aluminating close things brightly and object further away, not so brightly. The effect is reduced as the distances are increased.
If the distance is doubled, the effect of the force of gravity is one quarter of its original amount. Not only the distance, but the masses of the objects as well have an effect on gravity. Something even as small as a drinking cup has gravity, but is so small that the effect is not noticeable. Doubling the mass of an object will double the force of attraction to it. If the object is trebled in mass the attraction is all together six times its original value provided that the objects remain the same distance apart.

Someone standing on the Moon has less attraction to the Moon than someone standing on the Earth (about one sixth) because the mass of the Earth is six times the mass of the Moon. A man would therefore weigh more standing on the Earth.

Calculus is used when we wish to know the changes in which change itself is changing.

Stars are formed of mainly hydrogen and 25% helium and smaller amounts of other elements. The ratio of hydrogen to helium was set in the first 3 minutes of the Big Bang and is a severe test of the Big Bang dynamics.

As the explosive nuclear reactions energy (atomic nuclei) of a star pushes out, its gravity has an opposite effect holding this energy in . It is like a tug of war. Nuclear fusion proton-proton chain creates detrurium H2 (helium 2) where large amounts of energy is released. then to H3 (helium 3). The effect of this energy release causes the balance of the resulting helium to weigh less than the hydrogen it was formed from. This weight reduction has gone into energy (E = mc2). See Energy to Mass Conversion* equation.

The larger the star, the larger its gravitational force/field. When a gravity field which is so big, it can stop the light from escaping its gravity.

Once the fuel of a star is exhausted, it collapses under the weight of its gravity. If the star is significantly large enough, with gravity for which even light cannot escape, it is thought the star will become a 'Black Hole'.

On a greater scale, light can be bent by gravity. This was first realised, in theory, by Einstein and is called an 'Einstein Ring'. The ring is formed by the bending of light from the gravity of galaxies which are between us and the other galaxies which are further away. The light from the galaxies which are further away on the other side of the intervening galaxies, is bent from the huge gravitational forces they posses, bending the light around in an arc and in some cases magnifying the light like a lens. This technique has allowed us to see even further into the Universe.
The Einstein ring predication is thought of to be used as a lens for observing in the future. A method has already been used successfully to discover distance objects which have been magnified naturally by the gravitational effect.

A object which has a diameter of 5mm representing the size of the Sun, the nearest star would be 300km away. Now the 5mm is used to represent the size of our galaxy, the nearest galaxy is only 25cm away.

Gravitational forces can have an effect between galaxies as they come to close to each other, tear them apart into weird formations. However the chances of the stars and other matter colliding when they interact is very small because of the large distances between their stars.

ALBERT EINSTEIN (1879-1955)
German/American scientist, was one of the greatest contributors to modern physics.
Introduced the general and special theory of relativity and also large advances in quantum physics.

PROVING BIG BANG

Historical Meeting
The meeting of Einstein, Le Maitre and Hubble changed the face of the Universe all together. Einstein mentioned to Le Maitre that his physics was not very good, but Le Maitre was relentless in his pursuit in proving Einstein's theory wrong. With Hubble's observational prove and the theory brought together from both Einstein and Le Maitre, a great leap forward in cosmology took place. At the end of the meeting Einstein rose and proclaimed "this is the most beautiful thing I have ever seen".

GEORGE LE MAITRE
First proposed a 'primordial egg' from which the Universe expanded by using the second law of thermal dynamics as a starting point.

George Le Maitre, a Catholic Priest, challenged Einstein's belief of the steady state theory of the Universe (The Universe neither expanding nor collapsing). Einstein even introduced a cosmological constant (made something up) to fit his model of the Universe. Einstein commented "This is the biggest blunder of my life". Le Maitre, who was qualified in theology and mathematics, gave an account of the Universe having a beginning from a 'primordial egg' of atoms and expanding into what we see today. It was more a poetic description of the events, but is now accepted as how things started. Even after Einstein gave in, Fred Hoyle was still being the die hard in believing in the static (steady state) Universe.

The Universe expands like dots on a balloon as the balloon is blown up. The galaxies are moving further apart from each other without an increase in matter. Hubble's prove of an expanding universe implies that there must have been a beginning.

It is important to note that the Universe did not appear into pre-existing space, rather everything came from the Big Bang.

Effective ways to determine the aspects of the Universe can be done by looking at its past. When we observe far off galaxies, we are in effect, looking back in time as the light emitted by the galaxies takes time for it to travel the distance to get to us. The speed at which it travels is the speed of light. See Speed of Light* equation.

Time started with the Big Bang and so far it has been unreasonable to speculate what happened 'before' the Big Bang as this is where the laws of physics break down. So the origin of the Universe is not something to really contemplate, just the evolution.

STEPHEN HAWKING (1942- )
It's interesting to note that Isaac Newton was born in the year of Galileo's death and Stephen Hawking was born exactly 300 years after Sir Isaac Newton. Hawking holds Newton's Chair at Cambridge University. Hawking has worked on the basic laws which govern the Universe. His work with Roger Penrose, a mathematician, discovered through his mathematics the collapse of super massive stars will cause a black hole with a singularity. Steven Hawking applied this to the whole universe for his thesis. (an substantial, original, contribution to knowledge). Also with Penrose, they showed that Einstein's general theory of relativity implied space and time would have a beginning in the Big Bang and an end in black holes. These results indicated it was necessary to unify general relativity with quantum theory.

He also discovered 'Hawking effect'. "Black holes ain't so Black". He proved that some radiation particles could leave a black hole as the believe was that nothing could escape a black hole.

COSMIC BACKGROUND RADIATION (CBR)

SIR FRED HOYLE (1915-2001)
A British astronomer who became famous for his steady state theory of the Universe saying "Matter is continuously being formed in the Universe".

He later also believed that the universal constant of gravity may change with time, causing the weight of objects to change.

Fred Hoyle inaccurately described a static Universe and was supported by Dennis Sciama. Being persons of influence, many followed. "If new matter is being developed in an ever lasting steady state where is all this extra matter created?" This was a question Big Bangers wanted to know from the steady state theorists. A fundamental fuel was needed to create the new matter. Hoyle thought hydrogen was being created continuously throughout the Universe. This meant a new law of physics was needed to make this possible. Hoyle wouldn't give up his believe of the steady state and so challenged the Big Bang by saying "If there was a Big Bang (coined by him), there would be left over radiation to support this theory". This is what the Big Bang theorists started looking for.

David Wilkinson, Robert Dickie and a team at Princeton University, first set up the equipment, a small antennae, to search for CBR on Princeton University roof, but it took Bell Laboratory's Robert Wilson and Arno Penzias, who were trained radio astronomers, using a huge horn antennae, designed for the first satellite communications, to discover a strange noise wherever they pointed it. They could not find the supposed problem. Pigeons where found in the horn and they wondered if the droppings had an effect on this strange noise. The pigeons were removed and taken far away but unfortunately they were homing pigeons! A shot gun solved the problem! The noise was the CBR which Fred Hoyle had told the Big Bangers to look for to prove their case. The discovery of the CBR in 1965 and the fact that we see quasars at large distances, not older galaxies, showed that the Steady State theory disagreed with observation and was rejected. Because the background radiation was from all directions and that it had been found, it still didn't give the information of matter clumping together to form the stars and galaxies.

CBR Cosmic Background Radiation. The temperature of the left over radiation from the Big Bang would be by now at around the lowest temperature possible (-273o Celsius). It should therefore be possible to detect the is background radiation from all directions.

George Smoot realised a challenge beckoned to search for comparisons in temperature in the CBR. These minute differences would prove the Big Bang more accurately.

So, in 1989, George Smoot and his team watched as COBE, their specially designed Cosmic Background Explorer was launched amongst much anxiety of it working properly, also, if it would confirm what scientists thought they should find. It was a success! The success was announced on the 23rd of April 1992 after three years of collecting and sorting of data. It found tiny variations in temperature of the background radiation. It showed a now famous image of a non uniform early Universe where concentrations of matter where able to form galaxies and stars.

Some people still believe in the Steady State Universe and their opinions are widely recorded.

EDWIN HUBBLE (1889-1953)
In 1923, using the Hooker Telescope at Mount Wilson, the most powerful in the world at that time, discovered a way to determine distances to nearby galaxies. This work lead him onto spectral analysts thus creating firstly, an equation for the size of the Universe (the Hubble Constant) and secondly, proof for an expanding Universe.

Hubble used great strength and endurance in using the telescope night after night to guide and expose, up to a total of 40 hours, the whispy cloud formations in the night sky which at this stage were thought to be within our own galaxy - The Milky Way. At a guess, in his thesis, he thought the spiral shape of these clouds were like our own galaxy in formation, so he set out to prove they were outside our own galaxy.

Hubble's Determination of Distance
The distances of nearby galaxies can be determined by measuring the apparent brightness through a telescope. This enables us to estimate its distance by the diminished brightness. Conservation of energy tells us that the intensity of light diminishes as 1/distance2 (inverse square). This is because the energy at a distance is increasingly spread over the sphere of radius and a sphere has a surface of 4pD2. It is hard to work out each galaxy’s intrinsic brightness as all galaxies are different. So, Cepheid Variable stars within nearby galaxies are used instead. Studying Cepheid Variable Stars within our own galaxy, and using the inverse square rule on their brightness, can give us distances to other galaxies where their own Cepheid Variable Stars can be resolved. The distance of outer galaxies cannot be worked out accurately this way as the intrinsic brightness isn't a reliable indicator of brightness. The apparent distance is calculated only on what is called the 'standard candle' method.

Hubble's Cepheid Variable Stars
Taking photographs, at regular time intervals, show some Cepheid Variable stars alter their brightness with great precision. It has been discovered that a period of pulsation is equal to the intrinsic brightness of the star. A similar example of a Cepheid Variable’s pulsation corresponding to its brightness can be made by the flickering of fluorescence light. Fluorescence lights flickers very fast, so fast we cannot detect it with our eyes. A 30W fluorescence light will flicker a number of times, whereas, a 10W fluorescence light will flicker a different number of times. The Cepheid variables which have regular pulsations can be used to determine distance to nearby galaxies. Hubble found Cepheid Variables within the Andromeda galaxy and our own. Determining and verifying the distance of the Cepheid Variables in our own galaxy, using other methods (triangulation etc.) proved the accuracy of the method. Hubble went on to find other Cepheid Variables in the Andromeda galaxy to verify his distances. The comparisons of their brightness gave him the calculations to work out the distance of the Andromeda galaxy.

Although Hubble's measurement of the Cepheid Variables wasn't highly accurate due to it being a new determination, he never the less was accurate enough to calculate the distance to the nearest galaxies.

REDSHIFT

On Mount Flagstaff, Arizona, Percival Lowell created his dream by setting up a telescope with his own funds and resources to satisfy his love for astronomy. He gave a young man from his staff, Vesto Malvern Slyfer, a task to study objects which were thought to have been young solar systems within our galaxy, by using a prism to break up the faint incoming light into their colour light spectrum. This involved doing exposures of the faint objects over many nights. They did not expect to see what they found. The spectral lines were not where they should have been! They had shifted a large amount to the red end of the spectrum.

Hubble's Work with Redshifts
The distances of galaxies can be measured using what is similar to the Doppler effect. Instead of the Doppler effect of waves being used for sound, it is being used for light instead. Galaxies have been found to be moving away faster, the further away they are. This is consistent with the theory of Big Bang. The light spectrum of a galaxy moving appears different depending on how fast the galaxy is moving away from us. As in the Doppler Effect for sound, a fire engine siren will gain in pitch as it approaches the observer (the waves are being pushed together from the movement) and then suddenly drop in pitch as it passes the observer. The pitch is the same as blue on the colour spectrum to red as it recedes. The faster the galaxy is moving away the higher the Red shift of its light. Once the speed of the galaxy is known, the distance can be easily computed based on the data gained from nearby galaxies.

The hydrogen peak of the different galaxies can be measured from the spectrum of light displayed from a spectrometer attached to a telescope. Aided by computers, the information from the spectrum can be set-up to show red wave lengths of light are registered towards the right of the computer screen using a graph. The wave length of a 'nearby' galaxy is displayed showing the wave length of hydrogen peaking at the blue end of the light spectrum (to the left). The peak from hydrogen from a galaxy a lot further away will show up at the red end of the spectrum, to the right. Hence, the faster the galaxy is moving away from us, the further its hydrogen peak is moved towards the right end of the spectrum (red).

In 1923, Hubble, combined his own research with Slyfer's spectral discovery and realised he had found something which made an everlasting impact on cosmology.

Hubble made plots between his determination of apparent distances and the redshifts of the galaxies he studied. He did this by using the redshift minus the apparent distance. Here he found a relationship between the two. This was to determine that the galaxies where moving away from each other unlike the model Einstein had predicted which had the Universe in a static state. Einstein even introduced a cosmological constant (made something up) to make his fit his model of the Universe. Einstein commented that this was the biggest blunder of his life. Even after Einstein gave in, Fred Hoyle was still being the die hard in believing the static Universe.

Replacing redshift z with apparent velocity vapp in the plots for a number of galaxies leads us to the Hubble Constant Ho. This figure had the value of between 50km/sec/mpc to 100km/sec/mpc. Having the constant meant that this figure assumes to be the same throughout the Universe. However using the constant on distant galaxies showed to be inaccurate as the redshift of a galaxy which is 20mpc (mega parsecs) then if:

Ho = 50km/sec/mpc the apparent speed would be V = 50x20 = 1000km/sec

or:

a Redshift of z = v/c = 1000/3000,000 = 1/300 = 0.0033.

The distance can be worked out another way with Cepheid Variables in the same galaxy using the high resolution of the Hubble Space Telescope. The Hubble constant becomes 80+/-17km/sec/Mpc instead of 50km/sec/Mpc through plotting.

The constant determined using the dynamical models show this figure will decrease through time. See Age of Universe* equation.

It is important to realise that because nearby galaxies have gravitational forces which pull us towards each other. Their redshifts can be measured as negatives as they are in the blue part of the spectrum when measured. This is known as "peculiar motion" as a result of their shrinking wavelengths.

Hubble determined his equations from the data he had collected to fit the model of the Universe. The quandary of time and expansion still exists so instead we use the Universe itself as our preferred frame of reference instead of Hubble type plots. As the plots show, the Hubble Constant should remain the same anywhere in the Universe and the expansion should look the same as observed from any other galaxy. This implies a magnification effect as there is no centre to the Universe. The magnification scale factor of the Universe is called the scale factor. See Scale Factor R* equation. It is determined by comparing the sizes at earlier or later times with their present value. By the nature of magnification the size of any cosmological aspect of the Universe is enough for this purpose.

With this information we can estimate the age of the Universe. Improving the Hubble constant to make it really accurate will make an accurate age of the Universe possible. See Age of Universe* equation.

Literally over night, Hubble had turn the Universe into a much larger place, a factor of approx. 1,000,000,000!

Current estimated number of galaxies exceeds 100,000,000,000.

The plotting of the positions of some of the galaxies, an enormous task, was undertaken by the team of John Hoocra and Margaret Geller of the Harvard-Smithsonian Astrophysics Centre. Many thousands of galaxies have been mapped and when a section of this map is examined it shows the galaxies are strung out much like bubbles in a sink, but still being drawn together by their own gravity's.

OTHER BIG BANG TOPICS
Expansion forever or 'big crunch'? - How much dark matter, which we cannot see (doesn't give off any light), is in the universe?

- Quantum Physics - The study of sub atomic particles.

- General and Special Theory of Relativity.

- Hydrogen/helium models of the early Universe.

FINAL COMMENT

The topics discussed are the major discoveries to how we understand the Universe today. Using the high resolution of the Hubble Space Telescope, a more accurate figure for the Hubble constant is currently being obtained.

SOME INTERESTING FACTS

Largest Galaxy
The central galaxy of Abell 2029 galaxy cluster, 1070 million light years distant in Virgo has a major diameter of 5,600,000 light years - 80n times the diameter of the Milky Way announced in July 1990.

Furthest Galaxy
Furthest galaxy - radio galaxy 8C 1435+635 announced in May 1994. Redshift of 4.25 equivalent to 13,000 million light years. 14,000 million light years is thought to be the "observable horizon" where the speed of recession is equal to the speed of light or 1.32 x 10 power 23 km. 13,200 million light years is about 94.4% of this figure (furthest possible Quasar)

Most Massive Star
The variable star Eta Carinae, has a mass estimated at 150-200 times that of the Sun.

Least Massive star
Brown dwarf which has not enough mass to produce enough heat at the centre of the star to burn brightly is Gliese 229B. It has a mass of 20 and 50 times that of Jupiter. It is also therefore the dimmest star currently known.

Largest Planet in the Solar System
Jupiter has a mass of 317.828 times that of the Earth.

Smallest Planet in Solar System
Pluto has a mass of 0.0021 times that of the Earth.

EQUATIONS

Gravity's Acceleration
International agreed value for acceleration due to the Earth gravity is 9.80665 metres per second per second.

Newton's Law of Gravitation in Formula

Force = Gravity x mass1 x mass2r2

Light Diminishes

Intensity of light diminishes 1/distance2 due to increasing surface area.

Estimated Age of the Universe
Assuming the expansion rate has been the same using magnification method with Hubble's Constant.
Replacing Redshift z with Apparent Velocity v for the plots for a number of galaxies leads to the Hubble Constant Ho
From the Hubble plot there is a straight line relation v = Ho.D

Scale Factor
The straight Hubble's plot is used to explain centre-less expansion in Universe, which means the expansion has a magnification effect. The scale of the magnification is called the scale factor R. It is defined by comparing the sizes at earlier or later times with the present value.

R = Scale Factor

R = Some distance at time t : Dt
Same distance at time now to : Do

Using the magnification system and a random galaxy at a distance of:

D = 20Mpc converting to kilometres:

= 20 x 3.3 x 106 x 1013km

Using a Hubble Constant of 50km/sec/Mpc means the galaxy's present speed equals:

v = Ho.D = 50 x 20 = 1000km/sec

At a constant speed the galaxy would take a time t to travel the distance D:

t = D = 20 x 3.3 106 x 1013km = 33 x 1017sec = 20Gyr

v

1000km/sec 5
Hence Age of the Universe is to = 20Gyr

Instead of going through this each time, it is noticed that:

to alpha 1
Ho

so since Ho = 50 gives 20Gy, if gives a useful rule:

to = 50 x 20 Gy
Ho

changing Hubble's Constant Ho 50 100km/sec/Mpc, we get to = 10Gy

The effect of the galaxies gravity causing all the objects in the Universe to slow down can be estimated and taken into account:

to = 250 x 20 Gy, using a 2/3 factor = 15Gy

3 Ho

It is also useful to note the Hubble Constant can be affected by peculiar motions from nearby galaxies.
Present preferred figure for Ho is 80km/sec/Mpc. This gives the age based on these calculations as 8Gy with 2/3 de-acceleration factor built in.

Speed of Light
Sound travels at 670mph or 1072kph.
Light travels at 670 million mph or 1.1 billion kph. This also works out to be around 187,500 miles per second or 300,000 kilometres per second. If light at this speed travelled for one year, the distance would be around 9 460 350 000 000 kilometres, hence this amount is called simply 1 light year (l.y.). The parsec (pc) the other large distance unit is about 30 857 000 000 000 kilometres. 1 parsec = 3.26 l.y. The parsec is worked out by the distance at which a star would show a parallax of one second of arc. (trigonometry). It was first used in astronomy in 1832.
A typical galaxy can be 600 million light years away. This means we are observing the galaxy as it was 600 million light years ago.